What font is "z" in "z-score"?

Times font in both cases. The difference is italic versus upright. Kerning is slightly different if employed as math versus italic.

\documentclass{article}
\usepackage{newtxtext,newtxmath}
\begin{document}
$z$-score

\textit{z}-score
\end{document}

With MathTime Professional 2 fonts from PCTeX, complete or lite version, reading the guide to pag. 7, you can use in math-mode the "swash" z, putting into \usepackage[.....,lite]{mtpro2} the option zswash.

\documentclass[12pt]{article}
\usepackage[zswash,lite]{mtpro2}
\usepackage{newtxtext}
\begin{document}
$z$
\end{document}

This is the relative output.